Variability (or variation) in key process performance measures (such as measures of quality) is an extremely important aspect of most manufacturing processes. It is widely recognized that control of undesired variation can be instrumental in improving both process and product reliability. For example, consider the set of processing transformations illustrated in FIG. 2. The set of transformations depicted in FIG. 2 is referred to herein as a process or system. Each individual transformation is referred to as a subprocessing operation, or subprocess.
The inputs to each subprocess are the so-called signal and noise factors, while the output is termed the response variable. Although there may be more than one response variable of interest, consider the case of a single response from each subprocess. Changes in signal factors generally result in a relatively large change (or shift) in the response distribution, while noise factors represent (and thus contribute to) unavoidable and undesirable nuisance variation in the response variable.
There also is usually one or more control factors (or variables) associated with each subprocess shown as inputs to each “block”. Values (or settings) of these control factors can often be identified so that they minimize the unwanted and undesirable variation in the response.
Further, there are connections between subprocesses through which variation is transmitted or propagated throughout the system. In other words, this “coupling” of subprocesses represents the collection of pathways by means of which variation is transmitted downstream or upstream to connected systems. Note that the response from an upstream transformation may subsequently become either the signal or noise factor for one or more connected transformations.
For convenience and simplicity, only a single response from each subprocess is depicted in FIG. 2. The case of multiple responses represents a straightforward extension of the method to be described.
Several papers consider the propagation of process variation throughout a process having multiple processing stages. Fong and Lawless (1998) discuss a method for estimating the variation in product quality characteristics measured at multiple stages in a manufacturing process in which there are multiple measurements. The process considered is a linear assembly process required in the installation of car hoods. Lawless, MacKay and Robinson (1999) and Agrawal, Lawless and MacKay (1999) also discuss methods for analyzing variation in a multistage linear manufacturing process.
Gerth and Hancock (1995) describe the use of stepwise regression for determining which control factors should receive the most attention. They also consider where engineering efforts should be focused to better center the process mean or to reduce process variation.
Suri and Otto (1999A and 1999B) present an integrated system model based on the use of feed-forward control theory to reduce unwanted end-of-line variation in a manufacturing process. They argue that optimizing each subprocess individually (using such methods as Taguchi robust design methods or response surface methods) does not guarantee the lowest end-of-line variation. They consider system-level parameter design (i.e., the choice of control factor levels) in which the entire process is simultaneously optimized as a complete set. Each of the existing methods that addresses the problem of variation propagation through a series of manufacturing stages or subprocesses has one or more significant restrictions or shortcomings. In addition, none of these methods is nearly as robust nor as applicable to as many different situations likely to be encountered in practice as the method presented here.
The method of Lawless and Mackay (1999) is restricted to linear assembly processes, while that of Gerth and Hancock (1995) considers only the use of stepwise regression an a means for determining important process control variables. Suri and Otto (1999A and 1999B) explicitly require that the process behavior be linear in the region of local operating conditions.
The method according to the present invention has none of these restrictions and can be applied to both linear and non-linear processes. In addition, multiple response variables can be simultaneously considered. This method permits both means and variances to be modeled using either linear or nonlinear response models. The approach described herein completely accounts for the state-of-knowledge uncertainty and correlation between parameter estimates in all the fitted response models. Thus, the desired system output reflects all relevant sources of uncertainty.
Finally, there are no restrictions on how the subprocesses can be coupled. In summary, the present invention permits the simultaneous consideration of signal, noise, and control variables for both subprocess means and variances of coupled linear or non-linear subprocesses. Together, these represent a significant advancement over existing methods.
Although the present invention is directed to the same overall objective, a straightforward and simple-to-use statistical method based on the use of response models is presented.
Various features of the present invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.